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This dissertation is concerned with the Trapezoidal Product Integration Method to resolve Generalized Abel Linear Integral Equations of first -kind. Special attention is given to theorem of the convergence of the trapezoidal method. Mathematical results and a discussion about the existence and uniqueness of the solutions of the Generalized Abel Linear Integral. Equations are presented in chapter one. Theorems related with the convergence of the trapezoidal method are shown in chapters two and three. In chapter four it is analized the implicit backward difference product integration methods, proved its convergence,and also it is applied a sufficient condition to the root condition of the trapezoidal method. Numerical result is shown in chapter five.